Geodesic
On the primitivity of group algebras of certain classes of soluble groups of finite rank
Sbornik. Mathematics, Tome 186 (1995) no. 3, pp. 447-463

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper it is proved in detail that the group algebra $kG$ of a finitely generated metabelian group $G$ of finite rank over a field $k$ of characteristic zero is primitive if and only if its $FC$-centre $\Delta(G)$ is trivial. 
@article{SM_1995_186_3_a8,
     author = {A. V. Tushev},
     title = {On the primitivity of group algebras of certain classes of soluble groups of finite rank},
     journal = {Sbornik. Mathematics},
     pages = {447--463},
     publisher = {mathdoc},
     volume = {186},
     number = {3},
     year = {1995},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1995_186_3_a8/}
}
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A. V. Tushev. On the primitivity of group algebras of certain classes of soluble groups of finite rank. Sbornik. Mathematics, Tome 186 (1995) no. 3, pp. 447-463. http://geodesic.mathdoc.fr/item/SM_1995_186_3_a8/